#### Solutions

z = −1 + i nα = θ + 2πk u = ρ (cosα + isinα) f(x) = 3x − 2 2x + 2y + z + 4t = 0 −x + 2y + z + t = −1 nα = θ + 2πk   #### Best Match

Knowing how to respond to customers quickly and with a high degree of customization is a differentiating competitive factor.

z = −1 + i' nα = θ + 2πk u = ρ (cosα + isinα) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} z = −1 + i nα = θ + 2πk   #### Predictive Maintenance

How to improve the planning of maintenance interventions, so as to limit the impact on production and improve the service offered to customers.

C = {z = x + iy x, y ∈ IR} 2x + 2y + z + 4t = 0 z = −1 + i nα = θ + 2πk −x + 2y + z + t = −1 a (f(x + T) = f(x), ∀ x ∈ IR) (f(−x) = f(x), ∀ x ∈ D) nα = θ + 2πk   #### Workforce Scheduler

Analyze different scenarios to find the one that best resolves the trade-off between costs and service level for scheduling staff schedules.

a (f(x + T) = f(x), ∀ x ∈ IR) (f(−x) = f(x), ∀ x ∈ D) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} 2x + 2y + z + 4t = 0 nα = θ + 2πk −x + 2y + z + t = −1   #### Real Time Monitoring & Anomaly Detection

Monitor and anticipate phenomena that influence the evolution of a process or the life of a product.

a (f(x + T) = f(x), ∀ x ∈ IR) (f(−x) = f(x), ∀ x ∈ D) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} [x0 −r, x0 + r] (cosnα + isinnα) = (cosα + isinα)n z = −1 + i nα = θ + 2πk   #### Document miner

Navigate quickly and interactively within large document archives.

x + by + cz + d = 0 a (f(x + T) = f(x), ∀ x ∈ IR) (f(−x) = f(x), ∀ x ∈ D) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} z = −1 + i nα = θ + 2πk   #### Response Prediction

Identify which users of a service are at the highest risk of churn.

x + by + cz + d = 0 a (f(x + T) = f(x), ∀ x ∈ IR) (f(−x) = f(x), ∀ x ∈ D) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} z = −1 + i nα = θ + 2πk   #### Network Time-Series Forecasting

Monitor the functioning of every single element of a complex network.

z = r (cosθ + isinθ) x + by + cz + d = 0 (f(−x) = f(x), ∀ x ∈ D) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} z = −1 + i (f(−x) = f(x), ∀ x ∈ D)   #### Data-Driven & What If Analysis

Assign each entity of interest to a class.

(f(−x) = f(x), ∀ x ∈ D) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} z = −1 + i nα = θ + 2πk 2x + 2y + z + 4t = 0 z = −1 + i   #### Marketing Campaign Planning & Evaluation

Analysis, attribution and simulation of marketing campaigns.